Infinity & "Greater Infinities"

So, recently I was thinking about multiple universes (thanks in no small part to the awesome gift from my sister this Christmas - "Sliders" seasons 1 and 2 on DVD), and I came to a realization of something I was taking for granted in all my thought experiments on multiple quantum universes.

I always say that there is an infinite number of such quantum universes - since, without there being any "smallest unit of measurement" (you can always divide any distance in half), an electron when it jumps its orbit could appear in an infinite number of similar, but slightly different, locations around the nucleus - which would mean that everything affected by quantum universes with only that as different would also number in the infinite.

However, there are a near-infinite number of electrons and other chaotic occurances in the universe, which leads to something I've come to call "greater infinity" - basically, infinity times infinity = greater infinity.

How do infinity and greater infinity differ? Simply in that greater infinity approaches infinity faster than regular finity. 4x, where "x" can be any number, approaches infinity faster than 2x (in fact, it approaches it at twice the speed), and so could be said to be the "greater" infinity.

If you were to time-travel into the past (so you reduce probabilities instead of increase them), you WILL arrive at the correct past - but travelling into the future could bring in an infinite number of different chaotic occurances which may or may not affect the future you arrive at.

Such things as an electron changing where it re-appears in the universe (after leaving the energy state it was originally in around an atom) could be noted as "small infinities". They don't really affect the future you're arriving at. Their influence on things is smaller, even though there are an infinite number of universes where it is different.

However, your being in the past will create a "big infinity" - it's something that could dramatically change the future, as more big/real changes occur from your human interactions. This would be a greater infinity than the electron jump.

So, if we were to time-travel, would we have to work out a mathematical system with these big and small infinities to know where we're going? Would we have to plot these infinities on some kind of infinite grid? I don't know - just ideas I was having.


Now, next, I was thinking some more on the subject of the "smallest unit of measure". We know that one does not exist, as you could keep dividing the space between point A and point B in half. Perhaps this is not a problem of spacial reality because our 3 dimensions, as in string theory, curve into some other dimension. Once we divide small enough, we would enter this other dimension. Now, this dimension MAY have a smallest unit of measure (in whatever it's dimensional equivilant is), or it may not, but will somehow curve back into other dimensions as well. Perhaps this then curves again eventually back into OUR spacial dimensions.

This would mean that there both is and isn't a smallest unit of measure - something of a cosmic mobius strip that keeps this universe of ours in motion.

Thoughts? Comments? Observations? Ridicules ?

I am disgruntled at the moment, but I think this part of ATS is plagued with too many of these 'my theory' threads. It be great to see some math to back your claim or if you would use some sources with some math. I don't know linear algebra or claim to but it is just reasuring to see it so that the thread doesn't just become another philosophic concept of 'this could happen' or 'that could happen'.

Honestly I do not know what quantum physics has to do with infinite universes. I have never studied qp but I have read about it and read it in chemistry a few times, but I do not see what the universes have to do or dimensions have to do with qp. Could you provide some material on this subject. Or add it to the stickies because I cannot find anything there.

Sounds like stuff i have seen on NOVA: The Elegant Universe. It explained the theroy of relativity, quantum mechanics, and how they both related to the string theory. very interesting stuff. but the thing is, it only explained the concept of the theories and showed how they work through animation and examples. The math behind this stuff is really complex, from what iv'e seen and heard. I really want to learn it though, but my physics class is stuck with the very simple math of motion problems, so it looks like it will be a while before i learn the math to fully understand the string theory.

56, I know how you feel man. Back when I was in High School Physics they taught us pretty useless stuff on motion and changes in energy and such. It was only once I was in Grade 12 Physics (I was in the double-cohort year in Ontario, so Grade 13 didn't exist for us as it did for the students a year ahead of us) that we started learning interesting things and new theories and models. Quantum Physics and General Relativity was my FAVOURITE part - and if you stick in your physics class, though that section will be short, it will be deeply rewarding to finally get into some of the math behind it .

For Frosty, I know how you feel too. Many people have been posting things that are not based or grounded in any sort of rational thinking. They say things which are about as logical as saying "If metal sinks, and ship is made of metal, then the ship should sink". Unfortunately, there are some theories on ATS that are ahead of their time, and are equally beyond normal logic, but do make sense. Basically, a metal ship floats because of the way it's shaped - the person that discovered that realized there was more to physical properties than just basic deductive reasoning - there was also a visually observed effect of something new called "shape".

So, for maths on my ideas that I've presented here (I'm not calling this a theory yet, since I haven't been able to make any kind of base for it), I would have to ask you to take a look at the Cartesian Grid. Take the equation x^2. It starts at (0,0), then goes to (1,1), then (2,4), (3,9), (4,16), (5,25), and basically increases at an increasing rate. When X becomes infinity, the y-coordinate also becomes infinity. However, is there such a thing as infinity minus 1? Basically, it would be any number in infinity, minus one, or x-1. If x=infinity, and you could have infinity-1, then x could equal infinity-1, and therefore be (infinity-1)^2. Now, that would therefore be a greater number (or a "greater infinity") than infinity-1. Any number chosen in (infinity-1)^2 will be greater than infinity-1 if the number chosen is the same in both infinities.

Are you following?

Basically, I'm not asking for new math, or new solutions - but rather for a different way of percieving the way you normally view numbers. Doing so could probably do a lot for many equations or phenomena that depend on infinite numbers - such as black holes, time, and universal origins.

Now, as for what quantum physics has to do with infinite universes, well - take this idea.

You have a bunch of CDs all stacked on each other. A creature lives on the top one, and can't escape it. As far as that creature is concerned, there is only 1 CD. However, there could be any number of CDs in the stack. These CDs may even affect the top CD - but they're impossible to see, and so calculating or envisioning these CDs is nearly important.

The same thing may exist for our universe, but we have 3-dimensional space layered on other 3-dimensional space. Consider it to be the universe an atom's distance away from you at all times.

Now, quantum events depend on probabilities. You cannot "see" an electron - you can only predict where it is around an atom. It has a probability of being in a certain position. When an electron recieves enough energy to change orbits, it's probability for being anywhere inside the normal orbit instantly changes to 0%, and the probability of it being in a higher orbit becomes 100%. From our point of view we "see" the electron literally jump the distance between the first and second orbit WITHOUT PASSING THROUGH ANY SPACE INBETWEEN!

Supposedly, then, it is passing through some other kind of space that connects the two points - but not in any way that we can observe.

Now, String Theory then goes further and tries to examine this space that we cannot see. It's hit some bumpy roads, but it's progressively getting better. We are coming to a time where the universe as we know it does not exist just in the normal way we see it - but in countless miniature ways and forces that affect the very structure of existance.

56, as for this sounding like stuff you saw on NOVA, then I must say that is a big boost to my ego . I only came up with this idea myself - no outside influences involved. So thank you for the compliment. I look forward to advancements made in String Theory. I do not care whether my ideas or right or wrong so long as they stimulate others to think in ways that aren't considered the normal trend. It's in the questions that you can't answer that you find the greatest insights.

Originally posted by Yarium

However, is there such a thing as infinity minus 1?

I am not sure. It sounds like there would not be unless you are talking about an interval of the line.

Basically, it would be any number in infinity, minus one, or x-1. If x=infinity, and you could have infinity-1, then x could equal infinity-1, and therefore be (infinity-1)^2.

I could graph x^2-1. But I don't think that is what you are getting at is it. that would just be one value less than 0 on the y plane.

Now, that would therefore be a greater number (or a "greater infinity") than infinity-1. Any number chosen in (infinity-1)^2 will be greater than infinity-1 if the number chosen is the same in both infinities.

Are you following?

Yes I am following but where does this play into geometry? I was graphing equations like that not too long ago. Are you proposing something different than what a graphing calculator would accept?

You have a bunch of CDs all stacked on each other. A creature lives on the top one, and can't escape it. As far as that creature is concerned, there is only 1 CD. However, there could be any number of CDs in the stack. These CDs may even affect the top CD - but they're impossible to see, and so calculating or envisioning these CDs is nearly important.

The same thing may exist for our universe, but we have 3-dimensional space layered on other 3-dimensional space. Consider it to be the universe an atom's distance away from you at all times.

If you were trying to say that there are an infinite amount of universes that affect our own, would this provide a constant? Would this infinite affect ever allow us to know that it is there? That is what I made of it. But what makes anyone in the first place think it is a separate universe from ours?

It has a probability of being in a certain position. When an electron recieves enough energy to change orbits, it's probability for being anywhere inside the normal orbit instantly changes to 0%, and the probability of it being in a higher orbit becomes 100%.

Why? What caused the shift in numbers?

Originally posted by Frosty
Why? What caused the shift in numbers?

I'm not entirely sure of the specifics there. All I know is that they've determined that it's impossible for an electron to exist in the area inbetween the first and second orbit. In Quantum Theory, in Quantum Theory, with the probabilities of placement, since the electron can no longer occupy the space, it has 0% chance of being in that space.

To understand exactly why is either unknown, or you have to take a lot of courses to find out

Sorry I can't be of more help, but even my knowledge is limited

(sigh)

I agree with Frosty.

Basing theories on what you were taught in elementary school/junior high/high school is a poor idea. In fact, a great deal is known about infinity in a great many number of fields:
en.wikipedia.org...

What you are talking about has already been researched and is being researched in tremendous depth... this would be the aleph numbers, and concepts like the Hilbert Hotel, limits, continuum hypotheses, and so on and so forth into set theory (which is not what you learned in high school math. Trust me on this one) and beyond:
en.wikipedia.org...


Resources:
\mathforum.org...

Nice basic intro, including historical concepts and introduction to the large sets (cardinal sets, types of infinity, etc) :
www.mathacademy.com...

A middle-school level page about some of the interesting properties of infinities:
scidiv.bcc.ctc.edu...

simpler explainations:
www.math.toronto.edu...

fractals and infinity:
www.ainet.com...


When you have grasped the concepts and the research, then you'll be able to both read and understand (and work) the information in this article from 1987: www.dimi.uniud.it...

And you won't have any trouble with this article if you understand the concepts of infinity:
www.nbi.dk...

Thanks Byrd! I'm actually glad, as you said this has already been looked at. It means that I'm going along the right path on my own. I'll look into those infinity things you posted - hopefully it'll bring me further along my path.